Quantum Generalized Hydrodynamics of the Tonks-Girardeau gas: density fluctuations and entanglement entropy

TL;DR

This paper applies Quantum Generalized Hydrodynamics to derive precise analytical results for density fluctuations and entanglement entropy in a trapped Tonks-Girardeau gas after a trap quench, confirming predictions with numerical simulations.

Contribution

It extends QGHD to analyze density fluctuations and entanglement entropy in a quenched TG gas, incorporating conformal invariance and Fisher-Hartwig conjecture for universal and non-universal parts.

Findings

Analytical results match numerical simulations closely.

Universal behavior fixed by conformal invariance at the TG point.

Large Friedel oscillations require averaging to match theory.

Abstract

We apply the theory of Quantum Generalized Hydrodynamics (QGHD) introduced in [Phys. Rev. Lett. 124, 140603 (2020)] to derive asymptotically exact results for the density fluctuations and the entanglement entropy of a one-dimensional trapped Bose gas in the Tonks-Girardeau (TG) or hard-core limit, after a trap quench from a double well to a single well. On the analytical side, the quadratic nature of the theory of QGHD is complemented with the emerging conformal invariance at the TG point to fix the universal part of those quantities. Moreover, the well-known mapping of hard-core bosons to free fermions, allows to use a generalized form of the Fisher-Hartwig conjecture to fix the non-trivial spacetime dependence of the ultraviolet cutoff in the entanglement entropy. The free nature of the TG gas also allows for more accurate results on the numerical side, where a higher number of particles as compared to the interacting case can be simulated. The agreement between analytical and numerical predictions is extremely good. For the density fluctuations, however, one has to average out large Friedel oscillations present in the numerics to recover such agreement.